I'm not sure about your characterization of, or your answer to, the charge
that ID is not necessarily "God of the gaps" theology.

You say: It would be fair to label an I.D. argument as "god of the gaps" if
it said, for example, "If biological complexity can evolve, then atheists
will have won that territory. We won't be able to point to living organisms
as evidence of God's handiwork. However, there must be scientific evidence
of God's existence and miraculous action somewhere in nature, and the
complexity of life seems to be the best place to look for such evidence.
Therefore, biological complexity must be scientifically unexplainable."

But this doesn't seem like "God of the gaps" in the normal sense, it's more
like a grossly oversimplified religious pragmatism/apologetics. In other
words, what you've written above says, "we need to claim there are gaps in
biological history in order to preserve some room for a Creator God." While
there may be some who write in this fashion, boldly dictating their
scientific conclusion because of theological motive, the "God of the gaps"
conclusion that I've seen seems to be arrived at more indirectly.

It may start with a commitment to supernatural creation, but it proceeds to
an examination of complex features of nature that seem inconceivable to have
happened via only natural processes, so the conclusion is reached: "This
feature must have been done supernaturally, since science can't (and we
don't believe it ever will be able to) explain this using natural laws."
Thus a gap is created, where God is the default explanation because nature
won't suffice. This is classic "God of the gaps", as far as I know, and it
suffers from the problem that when science does find a natural explanation,
it appears to shrink the territory where God must have acted.

Yet, this is the view that you defend ID against as NOT being "God of the
gaps", when you wrote: "But we think - for scientific reasons, or
theological reasons, or both - that it is probably the case that God created
the universe in such a way that natural mechanisms are incapable of
producing biological complexity on their own, and that God chose to use
methods beyond normal natural mechanisms to produce the biological
complexity that we see. Therefore, we expect that scientists will not be
able to find a satisfactory explanation for how biological complexity could
evolve." Such an argument is neither "episodic deism" nor "god of the
gaps."

I'm not sure this answer exonerates ID from the charge in question. I'm not
even sure how to exonerate ID from the charge. If they made a more
temperate claim such as: "This particular feature looks to us like it must
be explained in terms of intelligence, but we are willing to reserve
tentative judgment in case future scientific discovery finds an explanation.
However, we believe there are plenty of areas where science will not be able
to provide all the answers, so the conclusion that there is an intelligent
designer is still a good hypothesis." Even here, this provides and even
acknowledges a steadily shrinking ground for God, which would be "God of the
gaps" if they hold to the claim on the basis that "natural" means excluding
God's governance by definition. However, if they made the claim that
natural but improbable mechanisms can still be held to be the result of
God's intelligent action (i.e. providence), that puts them more in line with
the explanation given by TE.